II. What are the chances?

The problem of randomness and determinism

If you throw a dice and it lands on 2, is that random or ‘all in the wrist’? What about when a computer generates a random number? What about when you run into an old friend on the street? We say “What are the chances!” There may be more to that statement than you think.

There are two kinds of randomness in the world around us with which we have to reckon: intrinsic (or ontological) randomness, and observed (or epistemological) randomness. Most things in life are ‘random’ in the sense that we can’t account for all the causes, and so we can’t predict the outcome, the same way ancients couldn’t predict eclipses. But just because they couldn’t predict eclipses doesn’t mean that eclipses are random. We call this observed or epistemological randomness, because borne from ignorance. Take the throwing of a dice as an example. If I knew all the relevant variables (the exact mass and shape of a dice, its velocity and rotation, how high it bounces, the air temperature, gravity, friction, etc.), I would be able to predict how it would land. But because I lack information and I remember the pain of undergrad mechanics and dynamics, I would rather conclude that there is a 1/6 chance for each number and be done with it. But actually, the dice throw is not intrinsically random, it’s deterministic.

As an aside, what about ‘random’ numbers generated by computer? They form part of encryption and many scientific investigations, and billions of dollars depend on such numbers. But as John von Neumann, the father of rocket science, remarked: anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin. (In case you were wondering, computers do arithmetic.) We have come much closer to true randomness since Neumann, but we’re still sinning. Computer-generated randomness is really just a sophisticated kind of observed randomness.

In 1814 the French mathematician Laplace realised what this determinism, where the world only seems to be random, but isn’t really, implies:

If an intelligence, at a given instant, knew all the forces that animate nature and the position of each constituent being; if, moreover, this intelligence were sufficiently great to submit these data to analysis, it could embrace in the same formula the movements of the greatest heavenly bodies in the universe and those of the smallest atoms: to this intelligence nothing would be uncertain, and the future, as the past, would be present to its eyes.

Laplace assumed that the second kind of randomness – that which is intrinsic to the system – doesn’t exist. This is where, even if you had all the information, you would still not be able to predict the outcome. At the moment the only instances of intrinsic randomness of which we are aware are quantum mechanics and human free will. And it was in this respect that Einstein, due to his reluctance in to accept quantum randomness, famously said that God does not play dice with the universe. Yet for all the possible randomness on the quantum (or even atomic) level, the rest of the world is still surprisingly regular; while individual neutrons (or people) may be unpredictable, thousands of them together are not. Although we can’t predict when a certain individual will have a motor accident, we can be sure that about 1000 South Africans will die on the roads this month. This is also how Carbon dating (used to determine the age of fossils) works: we don’t know when a given Carbon-14 atom decays to Carbon-12, but we know that if we have a million of them in a bone, half of them will decay within a given time. There is order even in the chaos.

The distinction between intrinsic and observed randomness is not relevant to statisticians: statistics is a practical, descriptive science, and more interested in the observed effect than in the nature of the randomness itself. But it does raise some interesting questions for the curious Christian. Is the universe a giant machine? Because it would seem that if all the ‘random’ events we observe have a scientific explanation, it leaves God no room to act. Would we then have to say that God only acts in the arena of quantum uncertainty or intrinsic randomness? Is this not a God-of-the-gaps argument? (That is, those arguments where God occupies the ever-shrinking gaps in our scientific knowledge.) Is there space for God in a practically non-random world? And where does all of this leave miracles? If God is responsible for this giant machine, does that not also make him responsible for all the pain, suffering and evil in the world?

We’ll have to cut it short here in order to keep things brief . Next time: randomness and divine providence. Fewer questions and more wild speculation!

2 thoughts on “II. What are the chances?

  1. Pingback: III. To the score of beautiful physics | Standard Deviations


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